What is the integral of xsin(3x-2) ?

The integral of xsin(3x-2) is -1/3 xcos(3x-2)+1/9 sin(3x-2)+C

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integral of xsin(3x-2)

\int x sin (3 x - 2) d x

- \frac{1}{3} x cos (3 x - 2) + \frac{1}{9} sin (3 x - 2) + C

Solution steps

\int x sin (3 x - 2) d x

Apply Integration By Parts

: - \frac{1}{3} x cos (3 x - 2) - \int - \frac{1}{3} cos (3 x - 2) d x

= - \frac{1}{3} x cos (3 x - 2) - \int - \frac{1}{3} cos (3 x - 2) d x

\int - \frac{1}{3} cos (3 x - 2) d x = - \frac{1}{9} sin (3 x - 2)

= - \frac{1}{3} x cos (3 x - 2) - (- \frac{1}{9} sin (3 x - 2))

Simplify

= - \frac{1}{3} x cos (3 x - 2) + \frac{1}{9} sin (3 x - 2)

Add a constant to the solution

= - \frac{1}{3} x cos (3 x - 2) + \frac{1}{9} sin (3 x - 2) + C

- cos (2 t)

\int 21 x sec^{2} (x) d x

\int \frac{1}{x ln ( x ) ln ( ln ( x ) )} d x

f (x) = 1 1^{x}

\frac{\partial}{\partial x} (\frac{x + y + z}{3})

What is the integral of xsin(3x-2) ?
The integral of xsin(3x-2) is -1/3 xcos(3x-2)+1/9 sin(3x-2)+C